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Computing and estimating information matrices of weak ARMA models

Author

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  • Boubacar Mainassara, Y.
  • Carbon, M.
  • Francq, C.

Abstract

Numerous time series admit weak autoregressive-moving average (ARMA) representations, in which the errors are uncorrelated but not necessarily independent nor martingale differences. The statistical inference of this general class of models requires the estimation of generalized Fisher information matrices. Analytic expressions are given for these information matrices, and consistent estimators, at any point of the parameter space, are proposed. The theoretical results are illustrated by means of Monte Carlo experiments and by analyzing the dynamics of daily returns and squared daily returns of financial series.

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  • Boubacar Mainassara, Y. & Carbon, M. & Francq, C., 2012. "Computing and estimating information matrices of weak ARMA models," Computational Statistics & Data Analysis, Elsevier, vol. 56(2), pages 345-361.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:2:p:345-361
    DOI: 10.1016/j.csda.2011.07.006
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    Cited by:

    1. Yacouba Boubacar Maïnassara & Landy Rabehasaina, 2020. "Estimation of weak ARMA models with regime changes," Statistical Inference for Stochastic Processes, Springer, vol. 23(1), pages 1-52, April.
    2. Bao, Yong & Hua, Ying, 2014. "On the Fisher information matrix of a vector ARMA process," Economics Letters, Elsevier, vol. 123(1), pages 14-16.
    3. Min, Aleksey & Czado, Claudia, 2014. "SCOMDY models based on pair-copula constructions with application to exchange rates," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 523-535.
    4. Christian Francq & Jean-Michel Zakoïan, 2013. "Estimating the Marginal Law of a Time Series With Applications to Heavy-Tailed Distributions," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(4), pages 412-425, October.
    5. Yacouba Boubacar Maïnassara & Youssef Esstafa & Bruno Saussereau, 2021. "Estimating FARIMA models with uncorrelated but non-independent error terms," Statistical Inference for Stochastic Processes, Springer, vol. 24(3), pages 549-608, October.

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    More about this item

    Keywords

    Asymptotic relative efficiency (ARE); Bahadur’s slope; Information matrices; Lagrange Multiplier test; Nonlinear processes; Wald test; Weak ARMA models;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics

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